Abstract
By the properties of the Musielak-Orlicz function's sequence, the necessary and sufficient condition for uniform Gateaux differential (UGD) property of Musielak-Orlicz sequence spaces equipped with the Luxemburg norm and a criterion for weakly uniform rotundity of Musielak-Orlicz sequence space with Orlicz norm are given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Smulian V L. Sur la derivabilite de la norme dans lescape de Banach[J].C R Acad Sci URBC (Doklady), N S, 1940,27(3):643–646.
Kaminska A. Rotundity of Orlicz-Musielak sequence space[J].Bull Acad Polish Sci Math, 1981,29 (3/4):137–144.
WANG Ting-fu, SHI Zhong-rui. On the locally uniformly weak star rotundity of Orlicz space[J].Revista Math Complutense, 1994,7(1):79–98.
Kaminske A. Strict convexity of sequence Orlicz-Musielak spaces with Orlicz norm[J].Journal of Functional Analysis, 1983,50(3):285–305.
Hudzik Henryk, YE Yi-ning. Support functional and smoothness in Musielak-Orlicz sequence spaces endowed with the Luxemburg norm[J].Comment Math Univ Carolinae, 1990,31(4):661–684.
Author information
Authors and Affiliations
Additional information
Communicated by ZHANG Shi-sheng
Foundation items: the National Natural Science Foundation of China (10001010); the Education Commission Foundation of Heilongjiang Province
Biographies: WANG Ting-fu (1933–2001); JI Dong-hai (1964-)
Rights and permissions
About this article
Cite this article
Ting-fu, W., Dong-hai, J. & Lian-ying, C. UGD property of Musielak-Orlicz sequence spaces. Appl Math Mech 24, 196–207 (2003). https://doi.org/10.1007/BF02437626
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02437626